Quantum reference frames beyond subsystems: a reconstruction and generalization of the perspective-neutral framework

Traditional quantum reference frame (QRF) frameworks often require that a reference frame be a physical subsystem (a tensor factor). This paper addresses the limitation of this assumption by asking how to define QRFs more generally, specifically when the frame is not a subsystem but rather a covariant quantum instrument. The authors aim to unify the operational (resource-theoretic) and perspectival (relational) approaches to QRFs.

Starting from an operational perspective, the authors define "completely covariant operations" as those that remain covariant even when extended to external systems. By reconstructing the perspective-neutral (PN) framework through this lens, they demonstrate that the requirement for complete covariance naturally leads to constraint equations (such as C|ψ⟩ = 0) on state vectors. They then generalize the PN framework to include covariant quantum instruments, which allows for the description of reference frames that do not correspond to specific subsystems.

This generalization provides a robust way to handle symmetries that do not act independently on subsystems. Key applications include:

• Indistinguishable Particles: The framework provides a natural explanation for the symmetrization postulate and the absence of parastatistics, while offering a clear description of entanglement between bosons and fermions.
• Relational Clocks: It allows for the construction of Page-Wootters clocks that reproduce the Schrödinger equation even in scenarios where all subsystems interact or where frequency superselection sectors are present.
• Constraint Quantization: The work provides an operational justification for constraint equations, bridging the gap between quantum information theory and the internal QRF research program.

By moving beyond the "subsystem" paradigm, this work provides a more flexible mathematical language for quantum gravity and gauge theories, where symmetries often do not respect simple subsystem partitions. It demonstrates that the perspectival nature of quantum mechanics can be grounded in operational principles, offering a unified view of how observers describe physical systems in the absence of an external, absolute reference frame.